On the regularity criteria of weak solutions to the micropolar fluid equations in Lorentz space

In this paper the regularity of weak solutions and the blow-up criteria of smooth solutions to the micropolar fluid equations on three dimension space are studied in the Lorentz space L(R). We obtain that if u ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 1 with 3 < p ≤ ∞; or ∇u ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 2 with 3 2 < p ≤ ∞; or the pressure P ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 2 with 3 2 < p ≤ ∞; or ∇P ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 3 with 1 < p ≤ ∞, then the weak solution (u, ω) satisfying the energy inequality is a smooth solution on [0, T ). AMS Subject Classification 2000: 35Q35,76W05, 35B65.